Quadratic Equations and Polygons

The lesson covers the study of angles and polygons, focusing on the relationship between the sum of interior angles and the size of exterior angles in a regular polygon. The teacher explains how to calculate these angles and solve for the number of sides using a quadratic equation. The solution reveals that the polygon is an octagon.

What is the main focus of the lesson on angles and polygons?

• Determining the number of sides of a polygon

• Identifying different types of polygons

• Finding the area of a polygon

• Calculating the perimeter of a polygon

Which formula is used to calculate the sum of interior angles of a polygon?

• n squared minus 2n

• 24 times the size of an exterior angle

• 180 multiplied by n minus 2

• 360 divided by n

How is the size of an exterior angle of a regular polygon calculated?

• 24 times the size of an interior angle

• n squared minus 2n

• 360 divided by n

• 180 multiplied by n minus 2

What is the relationship between the number of sides and the sum of interior angles?

• Equal

• Unrelated

• Inversely proportional

• Directly proportional

What relationship is given between the sum of interior angles and the size of exterior angles?

• The sum of interior angles is half the size of an exterior angle

• The size of an exterior angle is 24 times the sum of interior angles

• The sum of interior angles is equal to the size of an exterior angle

• The sum of interior angles is 24 times the size of an exterior angle

What type of equation is formed to solve for the number of sides of the polygon?

• Linear equation

• Quadratic equation

• Exponential equation

• Cubic equation

What is the first step in solving the quadratic equation for the number of sides?

• Subtract 180 from both sides

• Add 24 to both sides

• Divide by 360

• Multiply through by n

What is the simplified form of the quadratic equation after dividing by 180?

• n squared plus 2n plus 48 equals zero

• n squared minus 2n minus 48 equals zero

• n squared plus 2n minus 48 equals zero

• n squared minus 2n plus 48 equals zero

Which method is used to solve the quadratic equation in the lesson?

• Using the quadratic formula

• Factorization

• Completing the square

• Graphing

What are the two factors obtained from the quadratic equation?

• n minus 8 and n plus 6

• n plus 6 and n minus 8

• n plus 8 and n minus 6

• n minus 6 and n plus 8